Practice question

**Magnetic dipole in uniform field** experiences torque τ = m B sinθ and potential energy U = -m·B = -m B cosθ, minimum -mB when aligned (θ=0°), maximum +mB at anti-alignment (θ=180°). Work done rotating from θ₁ to θ₂ equals ΔU = mB(cosθ₁ - cosθ₂). B = μ₀ (H + M) , so H = (B/μ₀) - M . Given: B = 0.65 T , M = 4.5 × 10⁵ A m⁻¹ , μ₀ = 4π × 10⁻⁷ . (B/μ₀) = (0.65/4π × 10⁻⁷) ≈ 5.167 × 10⁵ A m⁻¹ . H = 5.167 × 10⁵ - 4.5 × 10⁵ = 6.67 × 10⁴ A